Lectures related to Kernel (linear algebra)

Explores Singular Value Decomposition, low-rank approximation, fundamental subspaces, and matrix norms.

Covers PCA, finding directions of largest variance, data dimensionality reduction, and limitations of PCA.

Linear Operators: Boundedness and Spaces

Explores linear operators, boundedness, and vector spaces with a focus on verifying bounded aspects.

Principal Component Analysis: Dimensionality Reduction

Covers Principal Component Analysis for dimensionality reduction, exploring its applications, limitations, and importance of choosing the right components.

What is a (sub)manifold

Introduces the concept of a submanifold in a linear space, defining it as a set smoothly embedded in the space.

Linear Algebra Basics: Matrix Representations and Transformations

Explores linear algebra basics, emphasizing matrix representations of transformations and the importance of choosing appropriate bases.

Principal Component Analysis: Applications and Limitations

Explores the applications and limitations of Principal Component Analysis, including denoising, compression, and regression.

Galilean Transformations: Spacetime and Measurements

Explores Galilean transformations in spacetime, focusing on measurements and coordinate transformations.

Smooth Manifolds: Diffeomorphisms

Explores smooth manifolds through diffeomorphisms and embedded submanifolds in a linear space.

Gaussian Elimination Method

Covers the Gaussian elimination method for solving linear equations using row operations on matrices.

Linear Algebra in Dirac Notation

Covers linear algebra in Dirac notation, focusing on vector spaces and quantum bits.

Differential Calculus: Applications and Reminders

Covers differential calculus applications and reminders, emphasizing the importance of differentiability in mathematical analysis.

Tutorial On Auto-encoders

Explores auto-encoders, covering invertibility conditions, projections, and generalized inverses in linear algebra.

Finite Elements: Variational Formulation

Explains the variational form in finite elements and the use of basic functions.

Finite Element Method: Quadrangular Elements

Explores basic functions and criteria in quadrangular finite elements using the finite element method.

Diagonalization in 3D Linear Algebra

Explores diagonalization in 3D linear algebra, covering conditions for diagonalizability and eigenvectors.

Geodesic convexity: why, and what we need

Explores geodesic convexity and its extension to optimization on manifolds, emphasizing the preservation of the key fact that local minima imply global minima.

Kernel Ridge Regression: Equivalent Formulations and Representer Theorem

Explores Kernel Ridge Regression, equivalent formulations, Representer Theorem, Kernel trick, and predicting with kernels.

Matrix Rank and Linear Systems

Explores matrix rank, subspaces, and their role in solving linear systems of equations.

Electrotechnique: Basics and Applications

Covers the basics of electrotechnique, including linear elements, current regimes, power types, and practical applications.